The Grander Question: The Rise, Fall and Rise Of The West
plusthe falls and rises of the Middle East, India, China, Central America...
The Grand Question looks pretty vast. In fact, the issue at stake is even larger, much larger. One must "not only" explain the astonishing success of the West in science & technology over the last centuries. One should also explain the astonishing regression of the West from 300 to 1100 (the Dark Ages), and its nonetheless amazing stagnation in the Roman times. And what about the Greek miracle? It needs as well an explanation: why did it start, why did it go on for four centuries, and why did it stop? Thus the mystery to unravel, the grander question, is, to put it shortly, the "rise-and-fall-and-rise" of the West.
In the same vein, a good theory should be able to shed light upon why Chinese science and culture flourished in Antiquity (Spring&Autumn and Warring States periods), then receded after 200, then flourished again after +200 for a few centuries, then crumbled around +1300, to take off again around 1890.
To put it shortly, one has to explain the rise-and-fall-and-rise of the West, as well as the rise-and-fall-and-rise-and-fall-and-rise of China... And the similar moves by India, the Middle East, the Central American civilizations... This we shall call the "Grander Question".

Ever grander questions
And there are other dimensions of flourishing of civilization to account of; not only scientific and technological, but as well artistic and social, even if
"technological creativity was at the very base of the rise of the West", as Joel Mokyr puts it (The Lever of Riches, p.vii). How is it that literature, music, painting underwent such flourishings, during both the Greek and the European miracles? And in the Middle Eastern, Indian, Chinese etc. miracle periods? Are science and the arts correlated, in some way? Or are they proceeding from the same causes?

The Need for a Grander Answer
In the end, what is needed is a Grander Answer to a Grander Question: Why does a civilization flourish, why does it recede? The issue is naturally of daunting difficulty, due to the sheer mass of information to manage.

Let's emphasize once again that there is much more to it than just the Grand Question of the West-Rest divergence after the XIVth century. Any theory willing to explain the rise of the West in the last centuries must in the end explain the other rises and falls of Western Europe and of the other civilizations. And there are many such mind-boggling evolutions throughout the history of civilizations. Instead of being embarassing exceptions (as they are in the realm of usual linear-progress view of history), periods of stagnation and falls will become nice testing grounds for candidate theories of the evolution of civilizations.

The Challenge
"Western technological superiority has deep historical roots, and can only be understood  if at all  by an analysis that is willing to look back centuries, even millenia" (Joel Mokyr, The Lever of Riches, p.vii)